Numerical Issues for a Non-autonomous Logistic Model
Explore the source record for details and available documents.
97 MATHEMATICS AND COMPUTING↗
SEARCH · Search NASA
Results for “Non-autonomous Model”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Fusing time-varying mosquito data and continuous mosquito population dynamics models
Climate change is arguably one of the most pressing issues affecting the world today and requires the fusion of disparate data streams to accurately model its impacts. Mosquito populations respond to temperature and precipitation in a nonlinear way, making predicting climate impacts on mosquito-borne diseases an ongoing challenge. Data-driven approaches for accurately modeling mosquito populations are needed for predicting mosquito-borne disease risk under climate change scenarios. Many current models for disease transmission are continuous and autonomous, while mosquito data is discrete and varies both within and between seasons. This study uses an optimization framework to fit a non-autonomous logistic model with periodic net growth rate and carrying capacity parameters for 15 years of daily mosquito time-series data from the Greater Toronto Area of Canada. The resulting parameters accurately capture the inter-annual and intra-seasonal variability of mosquito populations within a single geographic region, and a variance-based sensitivity analysis highlights the influence each parameter has on the peak magnitude and timing of the mosquito season. This method can easily extend to other geographic regions and be integrated into a larger disease transmission model. This method addresses the ongoing challenges of data and model fusion by serving as a link between discrete time-series data and continuous differential equations for mosquito-borne epidemiology models.
97 MATHEMATICS AND COMPUTING↗
Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Long-time uncertainty propagation using generalized polynomial chaos and flow map composition
We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The composition of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model
We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling
Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.
25 ENERGY STORAGE↗
Data-Driven Learning of Non-Autonomous Systems
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.
97 MATHEMATICS AND COMPUTING↗
A stochastic perturbation theory for non-autonomous systems
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimal control of wave energy converters
Optimal control theory is applied to compute control for a single-degree-of-freedom heave wave energy converter. The goal is to maximize the energy extraction per cycle. Both constrained and unconstrained optimal control problems are presented. Both periodic and non-periodic excitation forces are considered. In contrast to prior work, it is shown that for this non-autonomous system, the optimal control, in general, includes both singular arc and bang-bang modes. Conditions that determine the switching times to/from the singular arc are derived. Simulation results show that the proposed optimal control solution matches the solution obtained using the complex conjugate control. A generic linear dynamic model is used in the simulations. In conclusion, the main advantage of the proposed control is that it finds the optimal control without the need for wave prediction; it only requires the knowledge of the excitation force and its derivatives at the current time.
16 TIDAL AND WAVE POWER↗
Effective field theory of dark energy: a dynamical analysis
The effective field theory (EFT) of dark energy relies on three functions of time to describe the dynamics of background cosmology. The viability of these functions is investigated here by means of a thorough dynamical analysis. While the system is underdetermined, and one can always find a set of functions reproducing any expansion history, we are able to determine general compatibility conditions for these functions by requiring a viable background cosmology. In particular, we identify a set of variables that allows us to transform the non-autonomous system of equations into an infinite-dimensional one characterized by a significant recursive structure. We then analyze several autonomous sub-systems, obtained truncating the original one at increasingly higher dimension, that correspond to increasingly general models of dark energy and modified gravity. Furthermore, we exploit the recursive nature of the system to draw some general conclusions on the different cosmologies that can be recovered within the EFT formalism and the corresponding compatibility requirements for the EFT functions. The machinery that we set up serves different purposes. It offers a general scheme for performing dynamical analysis of dark energy and modified gravity models within the model independent framework of EFT; the general results, obtained with this technique, can be projected into specific models, as we show in one example. It also can be used to determine appropriate ansätze for the three EFT background functions when studying the dynamics of cosmological perturbations in the context of large scale structure tests of gravity.
79 ASTRONOMY AND ASTROPHYSICS↗
Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework
The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.
24 POWER TRANSMISSION AND DISTRIBUTION↗